Weird whining noise and no a/c

Right after I had the problem with the other weird noise coming from my steering column, I've found another problem.

The car sits outside in the sun for a couple minutes with the car off. The interior temperature in very hot. When I get in and turn it on, the weird electrical whining noise starts and the a/c doesn't turn on for about 10 minutes. The inside never cools down because there's no a/c. Then, I'm sweaty when I get to the place I need to be. What could this problem be? Please help! This has never happened before.